Scale Theory Mini-Course

In February and March 2013 I ran an online course called Introduction to Scale Theory with Appplications, in which I gave an elementary introduction to some of my theoretical interests aimed at practical musicians. I recorded three video lectures, which ended up being rather long, and ran Q&A sessions on reddit. This page preserves that information, so that if you missed it you can follow the course at your own pace. You can also contact me for in-person or Skype lessons covering this kind of material. I am also happy to run this course, or one like it, for groups of students.

Lecture 1: Foundations

The difference between a pitch, a note and a pitch class. The function of octave equivalence. Pitch class numbers. Two equivalent definitions of "scale". Transposition invariance of scales. Interval sequences. Modality and the definition of "mode".

Lecture 2: Classification

Binary representations of scales. Inversion and complementation as binary operations and their musical significance. How many scales are there? Classification by equivalence relation: cardinality, interval composition, modality and symmetry. Metrics on scales: Hamming distance and edit distance.

Lecture 3: Analysis

"Harmonization" of a scale from the root as a way to determine sound and likely applications of an exotic scale. Some basic notions from chord-scale theory. Applications of subsets and supersets of scales; generalisation of these ideas to the "spectra" of a scale.